First-principles calculations of the exchange coupling constants in La2CuO4

First-principles calculations of the exchange coupling constants in La2CuO4

ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 310 (2007) e264–e265 www.elsevier.com/locate/jmmm First-principles calculations of the ...

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ARTICLE IN PRESS

Journal of Magnetism and Magnetic Materials 310 (2007) e264–e265 www.elsevier.com/locate/jmmm

First-principles calculations of the exchange coupling constants in La2CuO4 G. Zheng, Kaihua He School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China Available online 30 October 2006

Abstract The exchanging coupling mechanism for La2 CuO4 has been studied by employing unrestricted Hartree-Fock (UHF) and configuration interaction method. The coupling constant J was calculated by using copper cluster models. It is shown that exchange interactions between the dx2 y2 orbitals play a very important role in the exchange coupling of La2 CuO4 and O to dx2 y2 excitations have secondary important in the La2 CuO4 ground state. The coupling constant calculated in this work was in good agreement with the experimental value. r 2006 Elsevier B.V. All rights reserved. PACS: 75.30.Et; 75.10.b; 71.27.þa Keywords: Exchange coupling; La2 CuO4 ; First-principles

1. Introduction Copper oxides are representative of classes of materials which have attracted a lot of theoretical and experimental interests in the past two decades. Depending on the amount of doping, they show many fascinating properties that open the possibility of technological applications. La2 CuO4 is a Mott insulator that orders antiferromagnetically. At low temperature, it has a space group of I4/mmm with ˚ c ¼ 13:157 A˚ (see Fig. 1). Its structure involves a ¼ 3:80 A, planes of CuO2 separated by donor metal oxide layers and the mobile electrons are in the copper 3d orbitals. 2. Coupling mechanism Similar to the technique used for manganites [1–3], the exchange coupling constant was calculated using the first principles configuration interaction (CI) calculations on a Cu2 O18 cluster terminated by copper pseudopotentials 11 and surrounded by a large array of point charges, with magnitudes obtained from unrestricted Hartree-Fock (UHF) calculations. The orbital bases used for the cluster Corresponding author. Tel.: +86 27 63442635; fax: +86 27 67883091.

E-mail address: [email protected] (G. Zheng). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.164

CI calculations were generated by self-consistent field generalized valence bond simulations. In our calculations, CI wave functions were constructed from the localized orbitals. A triplet state for the two-copper cluster Cu2 O18 11 ctriplet ¼ Aðfcoregðfx2 y2 ;l fx2 y2 ;r ÞðaaÞÞ,

(1)

where A is the anti-symmetrising operator, l or r on eg orbitals indicate that they are centered on the left or right Cu ion, fcoreg is a product of doubly occupied orbitals in the core orbital space. In general, CI wave functions with N electrons in the active orbital space consist of linear combinations of spinadapted functions (SAFs) X ci cSAF , ð2Þ cCI ¼ i i

cSAF i

¼ Aðfcoregfj fk . . . fs ft Ya Þ,

ð3Þ

where a SAF is a product of N singly occupied orbitals and a spin eigenfunction (SEF) [4], Ya , for the particular spin state in question. In this work, we employed the superexchange mechanism, X J ij Si :S j , (4) H ¼ hiji

ARTICLE IN PRESS G. Zheng, K. He / Journal of Magnetism and Magnetic Materials 310 (2007) e264–e265

e265

Fig. 2. UHF spin density plot for La2 CuO4 in the copper–oxygen plane.

Fig. 1. The crystal structure of La2 CuO4 in the panel (a). Shown in the panel (b) are the copper and oxygen orbitals in the Cu–O plane, arrows on the coppers denote the orientations of the spins.

where J ij is the exchange coupling constant. For the two Cu2þ cations, J is the energy difference between the singlet and triplet states. 3. Results and discussion A UHF spin density plot in the Cu-O plane of the unit cell was shown in Fig. 2. Through the superexchange mechanism, a strong antiferromagnetic coupling of the spins on the copper sites was found in the plane. The coupling constant, J, can be evaluated by using twocopper cluster Cu2 O18 11 calculation. If only one dx2 y2 in the active space, the coupling constant J ¼ 44 meV; however, if all the five 3d orbitals are included in the active space, J ¼ 87 meV. It was proved that a direct CI calculation with all localized Cu 3d and O 2p orbitals would result in the coupling constant a few meVs larger. For the four-copper cluster model, our calculations suggest J ¼ 125 meV [5], which is in good agreement with the experimental value of 138.3 meV [6] determined by highresolution inelastic neutron scattering. It is understood that the cyclic (ring) four-spin exchange [6,7] beyond the nearest-neighbor Heisenberg term have quite large influence on the coupling constant. The exchange coupling constant J of La2 CuO4 have been investigated using localized orbital first-principles

calculations on the specially designed clusters. By a detailed study of magnetic coupling constant J, we compare ab initio cluster model values with those in some manganites [1–3]. This comparison shows that exchange interactions between the dx2 y2 orbitals dominate in the exchange coupling of La2 CuO4 and O to dx2 y2 excitations have a lesser weight than Cu1þ Cu3þ in the La2 CuO4 ground state. The 3d orbitals have important influence on the coupling constant. Acknowledgments The authors thank C.H. Patterson, M. Liu and J. Zhang for helpful discussions. This work was supported by Enterprise Ireland (Contract No. SC00/267), Hubei Province Distinguished Young Scholars Funding (Contract No. 2006ABB031) and a CUG research funding (Contract No. 135141). References [1] [2] [3] [4]

G. Zheng, C.H. Patterson, Phys. Rev. B 67 (2003) 220404. C.H. Patterson, G. Zheng, J. Magn. Magn. Mater. 272–276 (2004) 124. M. Nicastro, .H C, Patterson, Phys. Rev. B 65 (2002) 205111. R. Pauncz, Spin Eigenfunctions: Construction and Use, Plenum, New York, 1979. [5] G. Zheng, K.H. He, M. Wan, unpublished. [6] R. Coldea, S.M. Hayden, G. Aeppli, T.G. Perring, C.D. Frost, T.E. Mason1, S.-W. Cheong, Z. Fisk, Phys. Rev. Lett. 86 (2001) 5377. [7] C.J. Calzado, C. de Graaf, E. Bordas, R. Caballol, J.-P. Malrieu, Phys. Rev. B 67 (2003) 132409.